Answer
$3(x - 4)(x - 2)$
Work Step by Step
Factor out the greatest common factor, which is $3$:
$3(x^2 - 6x + 8)$
The expression within parentheses is in standard form, which is $ax^2 + bx + c$.
Find factors that, when multiplied together, will equal $ac$, but when added together, will equal $b$.
In this expression, $a = 1$, $b = -6$ and $c = 8$; therefore, $ac = 8$.
Looking at the expression, both factors would have to be negative. Let's look at the possibilities:
$-4$ and $-2$
$-8$ and $-1$
Rewrite the expression in factor form:
$3(x - 4)(x - 2)$
Check the factorization with multiplication.
Expand the expression by multiplying the terms within them according to the FOIL method, meaning the first terms are multiplied first, then the outer, then the inner, and, finally, the last terms:
$3[(x)(x) + (x)(-2) + (-4)(x) + (-4)(-2)]$
$3(x^2 - 2x - 4x + 8)$
$3(x^2 - 6x + 8)$
$3(x^2) + 3(-6x) + 3(8)$
$3x^2 - 18x + 24$
This is the same expression that we started out with. Therefore, the factoring was correct.
